A Sample space is the list of all outcomes in a random experiment.

When it is impossible to list all

the outcomes, we create a model of the experiment. This is called simulation.

By simulating the experiment, we

will find the number of times a particular event or outcomes occur out of the

total number of trials. Based on this

we have a new definition of probability called Experimental definition of

Probability

Let A be an outcome of the random experiment . Then A is called an event.

The Experimental probability of the event A is given by

P(A) = Number of times the event occurs/ Total number of trials

Experimental probability is also known as Relative frequency

definition of Probability.

Lets consider a few examples

Example 1: -

A die is thrown 100 times out of which 5 appears 28 times. Find the experimental probability of getting the number 5?

Solution: -

The Experimental probability of the event A is given by

P(A) = Number of times the event occurs/ Total number of trials

Here die is thrown 100 times. So total number of trails =100

The number 5 occurs 28 times. So the number of times the required event

occurs = 28

Therefore

Example 2: -

A Box contains 15 red balls, 12 blue balls and 13 green

marbles. Find the experimental probability of getting a green ball.

Solution: -

The Experimental probability of the event A is given by

P(A) = Number of times the event occurs/ Total number of trials

Take a ball from the box. Note the color and return the ball.

Repeat a few times (maybe 200 times). Note the number of times a green ball

was picked (Suppose it is 120).

The experimental probability of getting a green ball from

the box is 120/200 = 60/100 = 0.6

Example 3: -

The following are the marks obtained by 1200 students in

a particular examination.

Marks: 100-120 120-140 140-160 160-180 180-200

No of 63 142 500 320 175

Students

Find the probability that a student selected has marks

(i) under 140

(ii) above 180

(iii) between 140 and 200

Solution: -

The Experimental probability of the event A is given by

P(A) = Number of times the event occurs/ Total number of trials

We can see that the total of the marks is 63 + 142 + 500 + 320 + 175 = 1200

(i) We have to find the probability that a selected student get marks under 40.

There are 63 + 142 = 205 students getting marks under 140.

Therefore P(student getting marks under 140)= 205/1200 =

(ii) We have to find the probability that a selected student get marks above 180.

There are 175 students getting marks above180.

Therefore P(student getting marks above 180) = 175/1200 =

(iii) We have to find the probability that a selected student get marks between 140 and 200.

There are 500 + 320 + 175 = 995 students getting marks between 140 and 200. Therefore P(student getting marks between 140 and 200) = 995/1200 =